Age Related Problems & Solution Part: 1

Question: 1 The sum of the ages of the son and father is 120 years. The father's age is 3 times than that of the son. What is the age of father?

Option: (a) 75 (b) 80 (c) 85 (d) 90
Explore: Let, the age of father be X years.
:. The age of son is (120 - X) years.
According to the question,
       3(120 - X) = X
=> 360 - 3X = X
=> 360 = X + 3X
=> 4X = 360
=> X = 360/4
=> X = 90
Answer : (d)

Question: 2 Lima is 10 years older than Rima. In 7 years time, Lima will be twice as old as Rima. Find Lima's age now?
Option: (a) 3 (b) 13 (c) 23 (d) 15 (e) 5
Explore: Let, now Lima's age be X years.
:. Rina's age is (X - 10) years
According to the question,
      X + 7 = 2{(X - 10) + 7}
=> X + 7 = 2(X - 3)
=> X + 7 = 3X - 6
=> 2X -X => 7 + 6
=> X = 13
Answer: (d)

Question: 3 Eight years age Mr. John was 1/3th the age he will be after 10 years.  What is his age now?
Option: (a) 16 (b) 17 (c) 18 (d) 19 (e) 20
Explore: Let, X be the age of Mr. John at present. According to the problem,
      X - 8 = 1/3(X 10)
=> 2X - 24 = X + 10
=> 2X = 24 + 10
=> X = 17
Answer: (b)

Question: 4 A father is 32 years older than the son. In 7 years the father's age will be 5 years more than twice that of the son. T he age of the father, 3 years from now, will be what?
 Explore: Let, son's age = X years
:. Father's age = X + 32
In 76 years, son's age = (X + 7) years
Father's age = (X + 32 + 7) years
                     = (X + 39) years
According to question,
      2(X + 7) + 5 = X + 39
=> 2X + 14 + 5 = X +39
=> 2X - X = 39 - 19
=> X = 20
:. Father's age = 20 + 32 = 52
:. 3 years from now, father's age 52 + 3 = 55 years
Answer : 55 years

Question: 5 A man's age is now 3 times his son's age. Eight years back, the man's age was 5 times his son's age. W hat is the present age of the son?
 Explore: Let, the present age of the son be X years.
:. The man's age = 3X years
According to the question,
      3X - 8 = 5X (X -8)
=> 3X - 8 = 5X - 40
=> 5X - 3X = 40 - 8
=> 2X =  32
=> X = 16
:. The present age of the son is 16 years

Question: 6 Father's age is presently double that of his son. 20 years earlier father's age was 4 times that of his son. What is the son's age now?
Option: (a) 10 (b) 30 (c) 25 (d) 20 (e) None
Explore: Let, X be the present age of the son. So, at present father's age is 2X
According to the problem,
      4(X - 20) = 2X - 20
=> 4 X -2X = 80 - 20 = 60
:. X = 60/2 = 30
Answer: (b)

Question: 7 A woman was 30 years old when her daughter was born, Her age is now 6 years more than three times her daughter's age. How old will the daughter be in 5 years?
Option: (a) 19 (b) 18 (c) 17 (d) 15(e) 14
Explore: Let, the present age of the daughter be X years. So, her mother's current age is (X + 30).
According to the problem statement,
(X + 30) = 3X + 6
:. 30 - 6 = 3X + 6
:. X = 24/2 = 12
:. In 5 years, the daughter will be 12 + 7 = 17 years.
Answer : (c)

Question: 8 Mr. Micle who is 28 has a son who is 4 years old. In how many years will Mr. Micle be 4 times as old as his son?
Option: (a) 1 (b) 2 (c) 3 (d) 4 (e) 5
Explore: Let, X be the required number of years. So, we may write
      28 + X = 4(4 + X)
=> 28 + X = 16 + 4X
=> 12 = 3X
=> X = 4
Answer: (d)

Question: 9 Asif is twice as old as Fafique, and karim is 6 years younger than Rafique. Four years age, Asif was 4 times as old as Karim. How old is Karim now?
Option: (a) 8 (b) 12 (c) 16 (d) 20 (e) None
Explore: Let, Karim be ?X years old now.
:. Rafique is (X + 6) years old.
& Asif is 2(X + 6) years old.
According to he problem,
      2(X + 6) - 4 = 4(X -4)
=> 2X + 12 - 4 = 4X - 16
=> 8 + 16 = 2X
=> X = 12
Answer : (b)

Question: 10 John is 10 years older than his brother Mike. However p years ago John was twice as old as Mike. If Mike is now N years old and N > p, find the value of n - p?
Option: (a) 10 (b) 11 (c) 12 (d) 13 (e) 14
Explore: Let, Mike age be s years and John age be r years.
:. John age is s + 10 years.
According to the question,
r = 10 + s
r - p = 2(s - p)
Given that Mike is now n years i.e s = n
:. r =  10 + n & r - p = 2(n - p)
:. 10 + n - p = 2(n - p)
:. 10 = n - p
Answer : (a)

Question: 11 Y is four times as old as X. After 6 years, the sum of half of X,s age and a fourth of Y,s age will be the same as three times the present age of X. How old will X be after 6 years?
Option: (a) 3 (b) 9 (c) 10 (d) 12 (e) 15
Explore: Let, X's age be X years and Y's age be Y years.
:. Y = 4X
According to the problem,
1/2(X + 6) + 1/4(y + 6) = 3X
:. 1/2(X + 6) + 1/4(y + 6) = 3X
Or, 1/2X + 3 + X + 3/2 = 3X
Or, 9/2 = 3X - (3/2)X = (3/2)X
Or, 3 =X
:. X + 6 = 9
Answer : (b)

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